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Simplifying 11y2 = y + 3 Reorder the terms: 11y2 = 3 + y Solving 11y2 = 3 + y Solving for variable 'y'. Reorder the terms: -3 + -1y + 11y2 = 3 + y + -3 + -1y Reorder the terms: -3 + -1y + 11y2 = 3 + -3 + y + -1y Combine like terms: 3 + -3 = 0 -3 + -1y + 11y2 = 0 + y + -1y -3 + -1y + 11y2 = y + -1y Combine like terms: y + -1y = 0 -3 + -1y + 11y2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.2727272727 + -0.09090909091y + y2 = 0 Move the constant term to the right: Add '0.2727272727' to each side of the equation. -0.2727272727 + -0.09090909091y + 0.2727272727 + y2 = 0 + 0.2727272727 Reorder the terms: -0.2727272727 + 0.2727272727 + -0.09090909091y + y2 = 0 + 0.2727272727 Combine like terms: -0.2727272727 + 0.2727272727 = 0.0000000000 0.0000000000 + -0.09090909091y + y2 = 0 + 0.2727272727 -0.09090909091y + y2 = 0 + 0.2727272727 Combine like terms: 0 + 0.2727272727 = 0.2727272727 -0.09090909091y + y2 = 0.2727272727 The y term is -0.09090909091y. Take half its coefficient (-0.04545454546). Square it (0.002066115703) and add it to both sides. Add '0.002066115703' to each side of the equation. -0.09090909091y + 0.002066115703 + y2 = 0.2727272727 + 0.002066115703 Reorder the terms: 0.002066115703 + -0.09090909091y + y2 = 0.2727272727 + 0.002066115703 Combine like terms: 0.2727272727 + 0.002066115703 = 0.274793388403 0.002066115703 + -0.09090909091y + y2 = 0.274793388403 Factor a perfect square on the left side: (y + -0.04545454546)(y + -0.04545454546) = 0.274793388403 Calculate the square root of the right side: 0.524207391 Break this problem into two subproblems by setting (y + -0.04545454546) equal to 0.524207391 and -0.524207391.Subproblem 1
y + -0.04545454546 = 0.524207391 Simplifying y + -0.04545454546 = 0.524207391 Reorder the terms: -0.04545454546 + y = 0.524207391 Solving -0.04545454546 + y = 0.524207391 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.04545454546' to each side of the equation. -0.04545454546 + 0.04545454546 + y = 0.524207391 + 0.04545454546 Combine like terms: -0.04545454546 + 0.04545454546 = 0.00000000000 0.00000000000 + y = 0.524207391 + 0.04545454546 y = 0.524207391 + 0.04545454546 Combine like terms: 0.524207391 + 0.04545454546 = 0.56966193646 y = 0.56966193646 Simplifying y = 0.56966193646Subproblem 2
y + -0.04545454546 = -0.524207391 Simplifying y + -0.04545454546 = -0.524207391 Reorder the terms: -0.04545454546 + y = -0.524207391 Solving -0.04545454546 + y = -0.524207391 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.04545454546' to each side of the equation. -0.04545454546 + 0.04545454546 + y = -0.524207391 + 0.04545454546 Combine like terms: -0.04545454546 + 0.04545454546 = 0.00000000000 0.00000000000 + y = -0.524207391 + 0.04545454546 y = -0.524207391 + 0.04545454546 Combine like terms: -0.524207391 + 0.04545454546 = -0.47875284554 y = -0.47875284554 Simplifying y = -0.47875284554Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.56966193646, -0.47875284554}
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